Polarobreathers in soft potentials

We consider polarons in models of coupled electronic and vibrational degrees of freedom, in the presence of a soft nonlinear inter-particle potential (Morse potential). In particular, we focus on a a bound state of a polaron with a breather, a so-called ``polarobreather''. We analyze the existence of this branch based on frequency resonance conditions and illustrate its stability using Floquet spectrum techniques. Multi-site solutions of this type are also obtained both in the stationary case (two-site polarons) and in the breathing case (two-site polarobreathers). We also obtain a different branch of solutions, namely a polaronic nanopteron.